Topological Invariants of 3-Manifolds with Boundary

2021/07/16 by Luca Di Beo, Di Beo, Luca
Computer Science · Mathematics · #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2107.07920

openalex publication_date 2021/07/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper presents, with explanatory details, the handle decompositions, fundamental groups and homology groups of 3-manifolds, including some knot complements. Hence, along this paper, when the word manifold appears it is implicit that its dimension is 3, except when explicitly generalized for n dimensions, n natural. The results were obtained for: 3-torus, projective space P³, trefoil (3¹), figure-eight (4¹), cinquefoil (5¹) and three-twist (5²).

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